NCMW - Sheaf Theory, Sheaf Cohomology and Spectral Sequences (2019)

Venue: Department of Mathematics University of Delhi, Delhi

Dates: 18 Nov 2019 to 30 Nov 2019


Convener(s)

 
Name: Prof Satya Deo Dr. Hemant Kumar Singh Dr Satya Prakash Tripathi
Mailing Address:  Harish Chandra Research Institute,
Chhatnaag Road, Jhusi, Allahabad- 211019
Department of Mathematics,
University of Delhi, Delhi-110007
Department of Mathematics,
Kirori Mal College, University of Delhi, Delhi-110007
Email: sdeo at hri.res.in
sdeo94 at gmail.com
hksinghdu at gmail.com
hemantksingh at maths.du.ac.in
drsptripathi at yahoo.com
satyapt93 at yahoo.com

Sheaf Theory is a very powerful tool for studying problems of algebraic Topology, algebraic Geometry, several complex variables and many other areas.of mathematics. The fundamental contributions made by H.Cartan, J.Leray and J-P Serre etc using the concepts of sheaf theory and sheaf cohomology are indispensable in the study of above subjects. Sheaf cohomology presents a unified approach to all kinds of cohomology theories.

Spectral sequences are generalizations of exact sequences. It was introduced by Jean Leray in 1946, and now have become important computrational tools, particularly in algebraic topology, algebraic geometry and homological algebra. In algebraic topology, for a pair of topological spaces (X, A), the relationship between certain homotopy, homology, or cohomology groups is expressed perfectly by an exact sequence. But for any sequence of spaces this relationship is very commplicated and a more powerful algebraic tool is needed, and the spectral sequences provides such a tool. Also, the Mayer-Vietoris sequence for a decomposition of a space X by two sets generalizes to a spectral sequence associated to a cover of X by any number of sets.

Discussion classes of the workshop will supplement and enhance the material covered in lectures along with problem solving.